It might make it easier to neatly subdivide everything like this, but the problem is that some of the methods that apply to dealing with rifles, slung rifles and pistols relate to each other. The underarm retention hold on a carbine is closely analogous to pistol techniques, and the use of a sling is a way of "holstering" a carbine to free your hands - but you can't really do both with a carbine at the same time.Exactly! This isn't a rifle vs handgun debate. That would be a separate argument.
Times change and different techniques go in and out of favor. 20 years ago Delta spent a huge amount of time and ammo using .45s as primary house clearing weapons, even though SBRs and subguns were available to them. Everyone has shifted to using carbines because the rounds are so much more effective - and also because a carbine is not a specialized piece of gear that stops being useful when you are back patrolling a street. But offensive handgun program stuff keeps popping up in SF because there are situations where shoulder fired weapons aren't the right solution.
Solving the HD problem requires understanding how any of the normal weapon options are going to function and evaluating why you're choosing one solution with all its limitations.